(x)=3x(4x+2)5

Solution for (x)=3x(4x+2)5 equation:

(x)=3x(4x+2)5

We move all terms to the left:

(x)-(3x(4x+2)5)=0


We calculate terms in parentheses: -(3x(4x+2)5), so:

3x(4x+2)5

We multiply parentheses

60x^2+30x

Back to the equation:

-(60x^2+30x)


We get rid of parentheses

-60x^2+x-30x=0

We add all the numbers together, and all the variables

-60x^2-29x=0

a = -60; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-60)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-60}=\frac{0}{-120}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-60}=\frac{58}{-120}
=-29/60
$